libigl/include/igl/curved_hessian_energy.h

// This file is part of libigl, a simple c++ geometry processing library.
//
// Copyright (C) 2020 Oded Stein <[email protected]>
//
// This Source Code Form is subject to the terms of the Mozilla Public License
// v. 2.0. If a copy of the MPL was not distributed with this file, You can
// obtain one at http://mozilla.org/MPL/2.0/.
#ifndef IGL_CURVED_HESSIAN_ENERGY_H
#define IGL_CURVED_HESSIAN_ENERGY_H

#include "igl_inline.h"

#include <Eigen/Core>
#include <Eigen/Sparse>


namespace igl
{
  /// Computes the curved Hessian energy using the Crouzeix-Raviart
  ///  discretization.
  /// See Oded Stein, Alec Jacobson, Max Wardetzky, Eitan Grinspun, 2020.
  ///  "A Smoothness Energy without Boundary Distortion for Curved Surfaces"
  ///
  /// @param[in] V  #V by 3 list of mesh vertex positions
  /// @param[in] F  #F by 3 list of mesh faces (must be triangles)
  /// @param[out] Q  #V by #V Hessian energy matrix
  template <typename DerivedV, typename DerivedF, typename ScalarQ>
  IGL_INLINE void
  curved_hessian_energy(
    const Eigen::MatrixBase<DerivedV>& V,
    const Eigen::MatrixBase<DerivedF>& F,
    Eigen::SparseMatrix<ScalarQ>& Q);
  /// Computes the curved Hessian energy using the Crouzeix-Raviart
  ///  discretization.
  /// See Oded Stein, Alec Jacobson, Max Wardetzky, Eitan Grinspun, 2020.
  ///  "A Smoothness Energy without Boundary Distortion for Curved Surfaces"
  ///
  /// @param[in] V  #V by 3 list of mesh vertex positions
  /// @param[in] F  #F by 3 list of mesh faces (must be triangles)
  /// @param[in] E #F by 3 a mapping from each halfedge to each edge
  /// @param[in] oE #F by 3 the orientation (e.g., -1 or 1) of each halfedge
  /// @param[out] Q  #V by #V Hessian energy matrix
  template <typename DerivedV, typename DerivedF, typename DerivedE,
  typename DerivedOE, typename ScalarQ>
  IGL_INLINE void
  curved_hessian_energy(
    const Eigen::MatrixBase<DerivedV>& V,
    const Eigen::MatrixBase<DerivedF>& F,
    const Eigen::MatrixBase<DerivedE>& E,
    const Eigen::MatrixBase<DerivedOE>& oE,
    Eigen::SparseMatrix<ScalarQ>& Q);

  /// Computes the curved Hessian energy using the Crouzeix-Raviart
  ///  discretization.
  /// See Oded Stein, Alec Jacobson, Max Wardetzky, Eitan Grinspun, 2020.
  ///  "A Smoothness Energy without Boundary Distortion for Curved Surfaces"
  ///
  /// @param[in] V  #V by 3 list of mesh vertex positions
  /// @param[in] F  #F by 3 list of mesh faces (must be triangles)
  /// @param[out] E #F by 3 a mapping from each halfedge to each edge
  /// @param[out] oE #F by 3 the orientation (e.g., -1 or 1) of each halfedge
  /// @param[out] Q  #V by #V Hessian energy matrix
  template <typename DerivedV, typename DerivedF, typename DerivedE,
  typename DerivedOE, typename ScalarQ>
  IGL_INLINE void
  curved_hessian_energy(
    const Eigen::MatrixBase<DerivedV>& V,
    const Eigen::MatrixBase<DerivedF>& F,
    Eigen::PlainObjectBase<DerivedE>& E,
    Eigen::PlainObjectBase<DerivedOE>& oE,
    Eigen::SparseMatrix<ScalarQ>& Q);



  /// Computes the curved Hessian energy using the Crouzeix-Raviart
  ///  discretization.
  /// See Oded Stein, Alec Jacobson, Max Wardetzky, Eitan Grinspun, 2020.
  ///  "A Smoothness Energy without Boundary Distortion for Curved Surfaces"
  ///
  ///  @param[in] F #F by 3 list of mesh face indices into rows of V
  ///  @param[in] l_sq #F by 3 list of squared edge lengths of each halfedge
  ///  @param[in] E #F by 3 a mapping from each halfedge to each edge
  ///  @param[in] oE #F by 3 the orientation (e.g., -1 or 1) of each halfedge
  ///    compared to the orientation of the actual edge, as computed with
  ///    orient_halfedges. will be computed if not provided.
  /// @param[out] Q  #V by #V Hessian energy matrix
  template <typename DerivedF, typename DerivedL_sq, typename DerivedE,
  typename DerivedOE, typename ScalarQ>
  IGL_INLINE void
  curved_hessian_energy_intrinsic(
    const Eigen::MatrixBase<DerivedF>& F,
    const Eigen::MatrixBase<DerivedL_sq>& l_sq,
    const Eigen::MatrixBase<DerivedE>& E,
    const Eigen::MatrixBase<DerivedOE>& oE,
    Eigen::SparseMatrix<ScalarQ>& Q);

  /// Computes the curved Hessian energy using the Crouzeix-Raviart
  ///  discretization.
  /// See Oded Stein, Alec Jacobson, Max Wardetzky, Eitan Grinspun, 2020.
  ///  "A Smoothness Energy without Boundary Distortion for Curved Surfaces"
  ///
  ///  @param[in] F #F by 3 list of mesh face indices into rows of V
  ///  @param[in] l_sq #F by 3 list of squared edge lengths of each halfedge
  ///  @param[in] dA #F list of double areas
  ///  @param[in] E #F by 3 a mapping from each halfedge to each edge
  ///  @param[in] oE #F by 3 the orientation (e.g., -1 or 1) of each halfedge
  ///    compared to the orientation of the actual edge, as computed with
  ///    orient_halfedges. will be computed if not provided.
  /// @param[out] Q  #V by #V Hessian energy matrix
  template <typename DerivedF, typename DerivedL_sq, typename DeriveddA,
  typename DerivedE, typename DerivedOE, typename ScalarQ>
  IGL_INLINE void
  curved_hessian_energy_intrinsic(
    const Eigen::MatrixBase<DerivedF>& F,
    const Eigen::MatrixBase<DerivedL_sq>& l_sq,
    const Eigen::MatrixBase<DeriveddA>& dA,
    const Eigen::MatrixBase<DerivedE>& E,
    const Eigen::MatrixBase<DerivedOE>& oE,
    Eigen::SparseMatrix<ScalarQ>& Q);


}


#ifndef IGL_STATIC_LIBRARY
#  include "curved_hessian_energy.cpp"
#endif

#endif